In this paper we have discussed techniques to compute large deviation
functions of climatic observables. Direct estimation of large deviation
functions in a complex chaotic system is a delicate procedure that
needs care in properly checking the convergence of both the large
deviation limit and of the statistical estimators [1]}.
A simplistic analysis relying on visual arguments for the collapse
of the scaled functions on some seemingly well behaved function can
lead to wrong estimates, as the functions will indeed converge, but
to wrong values. In particular, wrong estimates may lead to think
that the available data were enough to go beyond the Gaussian regime,
while as we have seen there may be cases in which a more refined analysis
shows that non Gaussian behaviors can appear as an artifact of not
having properly studied the convergence.
